In this work, we propose a method to simultaneously perform (i) biometric recognition (\textit{i.e.}, identify the individual), and (ii) device recognition, (\textit{i.e.}, identify the device) from a single biometric image, say, a face image, using a one-shot schema. Such a joint recognition scheme can be useful in devices such as smartphones for enhancing security as well as privacy. We propose to automatically learn a joint representation that encapsulates both biometric-specific and sensor-specific features. We evaluate the proposed approach using iris, face and periocular images acquired using near-infrared iris sensors and smartphone cameras. Experiments conducted using 14,451 images from 13 sensors resulted in a rank-1 identification accuracy of upto 99.81\% and a verification accuracy of upto 100\% at a false match rate of 1\%.